“Adaptive meshfree approximation with PDE-greedy kernel methods”
Martedì 2 Dicembre 2025, ore 11:00 - Sala Riunioni 7B1 - Tizian Wenzel (LMU Munich)
Abstract
This talk deals with efficient kernel methods for meshless approximation for solutions of PDEs both on domains as well as manifolds. We discuss the importance of the choice of the collocation points, in particular by using greedy kernel methods. We introduce a scale of PDE-greedy selection criteria that generalizes existing techniques, such as the PDE-P-greedy and the PDE-f-greedy rules for collocation point selection. For these greedy selection criteria we provide bounds on the approximation error in terms of the number of greedily selected points and analyze the corresponding convergence rates. Finally we show how these methods can also be applied to parametric PDEs by the use of state-parameter product kernels.
